Local and Global Stability of Delayed Congestion Control Systems

Yueping Zhang, Dmitri Loguinov
2008 IEEE Transactions on Automatic Control  
Stability proofs of nonlinear congestion control systems under heterogeneous feedback delays are usually difficult and involve a fair amount of effort. In this paper, we show that there exist a class of congestion control methods that admit very simple proofs of asymptotic stability and allow control equations to be delay-independent. This is in contrast to most previous work, which requires that each flow (and sometimes each router) adapt its control-loop constants based on the feedback delay
more » ... nd/or the length of the corresponding end-to-end path. Our new congestion control method, which we call Max-Min Kelly Control (MKC), builds upon Kelly's original work in [3] and allows end-flows to be stable and fair regardless of network feedback delays or the number of hops in their end-to-end paths. Using basic matrix algebra and discrete control theory, we show MKC's local asymptotic stability under heterogeneous, directional feedback delays. We also offer a simple proof of its global asymptotic stability assuming constant feedback delay.
doi:10.1109/tac.2008.2007135 fatcat:pajrykpkubeqfpwe2cvvnmllbu